Hybrid function projective synchronization in discrete dynamical networks via adaptive control

Volume 10, Issue 11, pp 5593--5607 http://dx.doi.org/10.22436/jnsa.010.11.01

Publication Date: November 10, 2017 Submission Date: January 10, 2017

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Authors

Ghada Al-mahbashi - School of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia. M. S. Md Noorani - School of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia. Sakhinah Abu Bakar - School of mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia.

Abstract

In this paper, we study the hybrid function projective synchronization between coupled complex discrete networks with different dimensions. The hybrid function projective synchronization is achieved by designing an adaptive control method. Based on the designed controller and the Lyapunov stability theory, we derive sufficient conditions to realize the hybrid function projective synchronization with different nodes. Moreover, with the adaptive update law, an adaptive control gains are obtained. Furthermore, we examine different cases of outer coupling matrix of node dynamics. Finally, we provide numerical examples to show the effectiveness of the proposed control scheme.

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Keywords

• Hybrid function projective synchronization
• delay coupling and non-delay coupling
• discrete complex dynamical networks
• adaptive control

MSC

•  93C40
•  34D06

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